The 20th percentile corresponds to the "top" 20% of the distribution, i.e. the critical value [tex]z[/tex] such that
[tex]\mathbb P(Z\le z)=0.80=F_Z(z)\implies z={F_Z}^{-1}(0.80)\approx0.8416[/tex]
where [tex]F_Z(z)[/tex] is the CDF for a standard normal distribution.
